Refer this on how to use discriminant to solve such problems.
For the quadratic function $ax^{2}+bx+c=0$ to have positive value, the discriminant $b^{2}-4ac<$ $0$
So, on simplifying for the given function, we get $9$$a^{2}$ $<$ $4$ $\Rightarrow$ $a^{2}$ $<$ $\frac{4}{9}$ $\Rightarrow$ $-\frac{2}{3}$ $<$ $a$ $<$ $\frac{2}{3}$
Option C is the answer.